Question

(i) Express y = x2(square) – 7x + 12 in the form y = (x – h)(x – k).

Answer 1

Here is your answer

Answer 2

Answer :-

$( \frac{ - 7}{2} \: \: and \: \: \frac{ - 1}{4} )$

$y = {x}^{2} + 7x + 12$

$y = {x}^{2} + 7x + {( \frac{7}{2} )}^{2} - {( \frac{7}{2} })^{2} + 12$

$y = ( {x + \frac{7}{2} })^{2} - \frac{49}{4} + \frac{48}{4}$

$1( {x - \frac{ - 7}{2} }))^{2} + ( \frac{ - 1}{4} )$

The Equation :-

$y = 1 ({x - (\frac{ - 7}{2} })^{2} + (\frac{ - 1}{4} )$

Is in vertex form :-

$y = a ({x - h})^{2} + k$

With multiplier a=${1}$ and vertex:-

$h = \frac{ - 7}{2}$

$k = \frac{ - 1}{4}$